Question

are quadrilaterals abcd and efgh similar?
yes, quadrilaterals abcd and efgh are similar because a translation of (x + 2, y + 4) and a dilation by the scale factor of 2 from point d map quadrilateral abcd onto efgh.
yes, quadrilaterals abcd and efgh are similar because a translation of (x + 3, y + 4) and a dilation by the scale factor of 2 from point a map quadrilateral abcd onto efgh.
no, quadrilaterals abcd and efgh are not similar because their corresponding angles are not congruent.
no, quadrilaterals abcd and efgh are not similar because their corresponding segments are not proportional.

Explanation:

Step1: Analizar la traslación

Observando los puntos \(A(-1,1)\) y \(H(1,5)\), la traslación en \(x\) es \(1 - (-1)=2\) y en \(y\) es \(5 - 1 = 4\), es decir, la traslación es \((x + 2,y+4)\).

Step2: Analizar la dilatación

Tomando el segmento \(AB\) (longitud \(2\)) y \(HG\) (longitud \(4\)), la escala de dilatación es \(\frac{4}{2}=2\).

Answer:

Yes, quadrilaterals \(ABCD\) and \(EFGH\) are similar because a translation of \((x + 2,y + 4)\) and a dilation by the scale factor of \(2\) from point \(D'\) map quadrilateral \(ABCD\) onto \(EFGH\).